Hughes was given three life sentences for abducting their daughter from a tent in her uncle's garden and raping her twice before strangling her and throwing her body into the sea. The couple, from Great Budworth, Cheshire, were speaking publicly for the first time since he was sentenced at Chester Crown Court.
Chris Hook, 38, who heard police say after the trial that they had "kept a close eye on" Hughes for 16 years, said he felt strongly that the proposals for a paedophile register should be put in place and advocated displaying posters of offenders in their home towns.
He also said that, in Hughes' case, life must mean life.
"An innocent life, Sophie's, has been destroyed. We are left with a life sentence ourselves."
The Hooks felt no sense of victory at seeing Sophie's killer finally behind bars.
Mr Hook, an advertising executive, said the verdict was "what we expected" but he blamed a failure in the system for not identifying earlier that Hughes, a known paedophile, was a potential killer. Hughes had also been accused of assaulting several young girls in the three years preceding his attack on Sophie.
He said: "I firmly believe that the Home Secretary's proposals that are going through currently should be extended.
"Allowing the authorities to display posters of offenders within the community is one possible step forward." Mr Hook, 38, added: "Several months after it happened I was told that Hughes was basically a time bomb waiting to go off."
"The unfortunate thing for us, and particularly for Sophie, was that she was the trigger for that time bomb and it didn't need to be like that."
He said he and his wife, Julie, 35, were constantly asking themselves the question: "Why Sophie? Why us?"
Sophie's mother spoke movingly about the daughter she had lost. "Sophie enriched all our lives," she said. "She was bright, vivacious, full of fun, extremely caring and very loving. This is how we remember her."
Her elder sister Jemma, 10, her brother Joseph, six, and infant sister Ellie all missed her, Mrs Hook said.
"Naturally, all the children have been affected by the loss of Sophie, each in their own different way. They are, however, all able to talk freely about Sophie and continue to include her in whatever they do."
She said the children would say things to her such as "Sophie would choose this colour, Mummy", or "these are Sophie's favourite biscuits, Mummy", or "Do you think Sophie would like my new shoes?".
Asked how her family had coped with their loss, she said: "The deep pain and grief we have felt and will continue to feel is, quite honestly, beyond words.
"We have somehow coped because we have every reason to believe that Sophie never knew of her suffering.
"It is this belief that keeps us going throughout all our darkest moments."Reuse content